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In this report, we discuss market relations in the cattle and beef sector of the United States by setting up a sequence of optimization decisions taken by cattle feeders (producers, sellers) and meat packers (processors, buyers) to solve for the equilibrium supply and demand proportions in the contract market in a first stage given the respective degrees of risk aversion for the representative producer and processor. Subsequently we derive the impacts of contracts, namely impacts on the spot market price and the processors’ ability to exercise oligopsony power, in a second stage. Using a model for a fixed-price contract, the equilibrium proportions allocated to the contract market by producers and processors correspond to those in Buccola’s model of decisions under risk (1981). This model is extended to solve for the equilibrium in the case of unequal bargaining power between the producer and processor. The residual supply function is used to derive the spot market price through a conjectural variation model and we refer to the prominent Lerner Index for the downstream processor’s oligopsony power. We find that the use of fixed-priced contracts for risk averse producers and processors can serve to reduce the spot market price offered for cattle given the assumption that the residual supply becomes more inelastic. Hence, the processor enjoys higher oligopsony power in the spot market.
We run simulations in a spreadsheet model to derive further insights about key parameters, including the risk aversion coefficients, the spot market price variance, the coefficient of expectations, and the bargaining power weights in the contract market. We observe that when the spot market price is expected to be higher than the equilibrium fixed contract price, increases in the producer’s coefficient of risk aversion cause their optimal share of cattle marketed through contracts to increase and hence it contributes to a higher spot market price. On the other hand, when the expected market price is lower than the equilibrium contracted price, increases in the producer’s coefficient of risk aversion decreases the producers’ optimal share of cattle marketed through contracts relative to the processors’ and hence contributes to lower spot market prices. These two results are due to the fact that increasing risk aversion decreases the sensitivity with which optimal portfolios react to changes in the price parameters. By simulating increasing (decreasing) spot market price variance, we observe the equilibrium contracted proportions to increase (decrease) accordingly. In turn, this causes a lower (higher) spot market price. The simulations on the degree of the processors’ bargaining power in the contract market show that increases in the processors’ bargaining power induces higher demand for contracts by processors and lower supply of contracts by producers. This results in a decline in the contract price and an increase in the spot market price.
Finally, a brief exercise in a dynamic decision making reveals that a producer will always choose to contract out a proportion of their cattle as long as they are less than 50% certain that, on average, future market prices will be slightly lower than the offered contract price.